Details

analyze804.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample200.0ms (1.3%)

Algorithm

1×

intervals

Results

100.0ms	58×	body	2048	valid
54.0ms	83×	body	1024	valid
10.0ms	41×	body	512	valid
6.0ms	2×	body	4096	valid
5.0ms	8×	body	1024	invalid
4.0ms	12×	body	512	invalid
4.0ms	56×	body	128	valid
2.0ms	16×	body	256	valid
1.0ms	11×	body	128	invalid
1.0ms	3×	body	256	invalid
1.0ms	10×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify223.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	22
1	4939	22

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 46.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.0b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.6b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
12.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite202.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_1805`
486×	`add-sqr-sqrt_binary64_1821`
367×	`*-un-lft-identity_binary64_1799`
225×	`add-cube-cbrt_binary64_1834`
174×	`associate-r_binary64_1739`
168×	`difference-of-squares_binary64_1768`
88×	`unpow-prod-down_binary64_1878`
85×	`sqr-pow_binary64_1771`
84×	`difference-of-sqr-1_binary64_1769`
29×	`div-inv_binary64_1796`
28×	`distribute-lft-out--_binary64_1751`
19×	`add-exp-log_binary64_1837`
18×	`add-cbrt-cube_binary64_1835`
13×	`associate-/l_binary64_1744` `associate-/r_binary64_1743`
7×	`pow1_binary64_1860`
6×	`div-exp_binary64_1850` `add-log-exp_binary64_1838` `cbrt-undiv_binary64_1833`
3×	`prod-exp_binary64_1848` `pow-unpow_binary64_1876` `unswap-sqr_binary64_1767` `associate-l_binary64_1740` `cbrt-unprod_binary64_1832` `cancel-sign-sub-inv_binary64_1765`
2×	`flip--_binary64_1774` `associate-/r/_binary64_1745` `flip3--_binary64_1803` `associate-/l/_binary64_1746`
1×	`div-sub_binary64_1804` `sub-neg_binary64_1792` `clear-num_binary64_1798` `pow-to-exp_binary64_1868` `frac-2neg_binary64_1810` `associate-r/_binary64_1741` `diff-log_binary64_1891` `pow-exp_binary64_1867` `-commutative_binary64_1730` `pow-pow_binary64_1871` `pow-prod-down_binary64_1870` `distribute-lft-out_binary64_1750`

Counts

4 → 451

Calls

4 calls:

71.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
23.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
14.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
9.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series2.0s (13.2%)

Counts

4 → 12

Calls

4 calls:

613.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
553.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
540.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
296.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5117	14771

prune1.3s (8.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	453	10	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	454	10	464

Merged error: 20.2b

Counts

464 → 10

Compiler

Compiled 23034 to 13499 computations (41.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.3b	(*.f64 1/6 i)
18.3b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite71.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_1805`
97×	`add-sqr-sqrt_binary64_1821`
85×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
50×	`associate-r_binary64_1739`
25×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
13×	`pow1_binary64_1860` `associate-/r*_binary64_1743`
9×	`div-inv_binary64_1796`
7×	`prod-exp_binary64_1848` `associate-l_binary64_1740` `cbrt-unprod_binary64_1832`
6×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
5×	`unswap-sqr_binary64_1767` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838`
3×	`associate-/l_binary64_1744` `associate-r/_binary64_1741` `*-commutative_binary64_1730`
2×	`associate-/r/_binary64_1745` `associate-/l/_binary64_1746` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`distribute-rgt-in_binary64_1749` `clear-num_binary64_1798` `distribute-lft-in_binary64_1748` `frac-2neg_binary64_1810`

Counts

4 → 179

Calls

4 calls:

20.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
10.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
9.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series293.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
89.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
84.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
20.0ms	(*.f64 1/6 i)

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4928	5462
1	4928	5462

prune1.7s (11%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	181	20	201

Merged error: 7.8b

Counts

201 → 20

Compiler

Compiled 35529 to 23351 computations (34.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.1b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.3b	(*.f64 i 1/6)
1.7b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1821`
15×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
12×	`associate-l_binary64_1740`
11×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
10×	`associate-r_binary64_1739`
8×	`associate-*r/_binary64_1741`
6×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838` `*-commutative_binary64_1730`
3×	`unswap-sqr_binary64_1767` `flip3-+_binary64_1802` `flip-+_binary64_1773`

Counts

4 → 86

Calls

4 calls:

8.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
6.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
6.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
4.0ms	(*.f64 i 1/6)

series275.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
84.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
77.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
20.0ms	(*.f64 i 1/6)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4963	1381
1	4963	1381

prune251.0ms (1.7%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	4	15	19
Picked	0	1	1
Done	0	0	0
Total	99	19	118

Merged error: 7.8b

Counts

118 → 19

Compiler

Compiled 4929 to 3503 computations (28.9% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.1b	(/.f64 (.f64 (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6))))) (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))) i)
13.7b	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
13.7b	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
13.7b	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64_1831`
9×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `cbrt-prod_binary64_1830` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837` `flip3-+_binary64_1802` `flip-+_binary64_1773`
8×	`associate-/l/_binary64_1746`
7×	`add-cbrt-cube_binary64_1835`
4×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `frac-times_binary64_1809`
3×	`pow1/3_binary64_1881` `associate-/r*_binary64_1743` `times-frac_binary64_1805`
2×	`div-exp_binary64_1850` `associate-r/_binary64_1741` `cbrt-undiv_binary64_1833` `associate-l/_binary64_1742`
1×	`clear-num_binary64_1798` `associate-/l*_binary64_1744` `prod-exp_binary64_1848` `frac-2neg_binary64_1810` `cbrt-unprod_binary64_1832` `div-inv_binary64_1796`

Counts

4 → 68

Calls

4 calls:

12.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6))))) (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))) i)
3.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
3.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))))
3.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))

series350.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6))))) (cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))) i)
74.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))))
74.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))
64.0ms	(cbrt.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))))

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4848	2474
1	4848	2474

prune584.0ms (3.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	1	16	17
Picked	1	0	1
Done	0	1	1
Total	78	21	99

Merged error: 7.8b

Counts

99 → 21

Compiler

Compiled 12268 to 8545 computations (30.3% saved)

regimes167.0ms (1.1%)

Compiler: Compiled 1112 to 816 computations (26.6% saved)

bsearch163.0ms (1.1%)

Steps

Iters	Range		Point
8	0.0014931353196297825	2.08581718441891	0.12982209090675584
10	-43684.54863689671	-9.282008832417844e-13	-0.08077746953445203

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	89
1	62	89

end0.0ms (0%)

sample6.2s (40.5%)

Algorithm

1×

intervals

Results

2.8s	1781×	body	2048	valid
1.5s	2534×	body	1024	valid
355.0ms	1232×	body	512	valid
134.0ms	1856×	body	128	valid
109.0ms	165×	body	1024	invalid
97.0ms	33×	body	4096	valid
89.0ms	564×	body	256	valid
84.0ms	235×	body	512	invalid
43.0ms	456×	body	128	invalid
37.0ms	171×	body	256	invalid
27.0ms	20×	body	2048	invalid
17.0ms	327×	body	128	nan

Compiler

Compiled 669 to 485 computations (27.5% saved)

Details

analyze804.0ms (5.3%)

sample200.0ms (1.3%)

simplify223.0ms (1.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite202.0ms (1.3%)

series2.0s (13.2%)

simplify147.0ms (1%)

prune1.3s (8.4%)

localize11.0ms (0.1%)

rewrite71.0ms (0.5%)

series293.0ms (1.9%)

simplify109.0ms (0.7%)

prune1.7s (11%)

localize9.0ms (0.1%)

rewrite32.0ms (0.2%)

series275.0ms (1.8%)

simplify54.0ms (0.4%)

prune251.0ms (1.7%)

localize26.0ms (0.2%)

rewrite34.0ms (0.2%)

series350.0ms (2.3%)

simplify98.0ms (0.6%)

prune584.0ms (3.8%)

regimes167.0ms (1.1%)

bsearch163.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.2s (40.5%)

Profiling